Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization
of semibounded selfadjoint operators


Authors: Seppo Hassi, Michael Kaltenbäck and Henk de Snoo
Journal: Proc. Amer. Math. Soc. 125 (1997), 2681-2692
MSC (1991): Primary 47B15, 47B25
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a class of closed symmetric operators $S$ with defect numbers $(1,1)$ it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when $S$ is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator $A$ is semibounded if and only if each one-dimensional restriction of $A$ has a generalized Friedrichs extension.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47B15, 47B25

Retrieve articles in all journals with MSC (1991): 47B15, 47B25


Additional Information

Seppo Hassi
Affiliation: Department of Statistics University of Helsinki PL 54, 00014 Helsinki Finland
Email: hassi@cc.helsinki.fi

Michael Kaltenbäck
Affiliation: Institut für Analysis, Technische Mathematik und Versicherungsmathematik Technische Universität Wien Wiedner Hauptstrasse 8-10/114 A-1040 Wien Österreich
Email: mbaeck@geometrie.tuwien.ac.at

Henk de Snoo
Affiliation: Department of Mathematics University of Groningen Postbus 800, 9700 AV Groningen Nederland
Email: desnoo@math.rug.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03960-9
PII: S 0002-9939(97)03960-9
Keywords: Symmetric operator, selfadjoint extension, Friedrichs extension, $Q$-function, Nevanlinna function
Received by editor(s): April 22, 1996
Additional Notes: The second author was supported by “Fonds zur Förderung der wissenschaftlichen Forschung” of Austria, Project P 09832-MAT
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society